Why Rounding Is Sometimes Wrong: Significant Figures and Error Accumulation
Round at every step and the final result drifts. Understanding error accumulation and banker's rounding makes your calculations trustworthy.
Rounding is the first rule taught in school, yet in chained calculations or large datasets, mechanical rounding introduces systematic bias and accumulated error.
Problem one: don't round intermediate steps
Compute 1.4 × 2.6 × 3.8, rounding to one decimal each step: 1.4 × 2.6 = 3.64 → 3.6, then 3.6 × 3.8 = 13.68 → 13.7. Computed directly, 1.4 × 2.6 × 3.8 = 13.832 → 13.8. Rounding mid-way shifted the result by 0.1.
Problem two: rounding has systematic bias
Digits 1–4 round down and 6–9 round up, which looks fair, but the treatment of 5 gives one extra case to rounding up. Across large datasets that makes results systematically too high.
Statistics more often uses “round half to even” (banker's rounding): below 5 rounds down, above 5 rounds up, and exactly 5 goes to the nearest even number. Over many values, positive and negative biases cancel out.
- 2.5 → 2 (toward the even number)
- 3.5 → 4 (toward the even number)
- 1.24 → 1.2
- 1.26 → 1.3
What significant figures are
Significant figures are the digits counted from the first non-zero digit, and they express the precision of a measurement or calculation. 0.0052 has two significant figures; 5.20 has three. A trailing zero isn't decorative — it says that zero was actually measured.
Rules of thumb: for addition and subtraction, match the fewest decimal places; for multiplication and division, match the fewest significant figures.
Using it day to day
The Rounding Calculator handles a variety of rounding needs. Be especially careful with financial data: currency calculations typically specify two decimals, and you should round the final result rather than every intermediate amount.